A trait shared by many of the portraits is that they spend most of the time asleep or pretending to be asleep, though most of them, with the occasional exception of Phineas Nigellus Black, will immediately awaken when addressed.

Behind the scenes

It is possible that Dolores Umbridge does not have a portrait, because she is probably alive and only in azkaban.Most headmasters only receive their potraits once they die.Moreover Hogwarts did not recognise her as Headmistress. For example, she was denied access to the Headmaster's office.

According to J. K. Rowling, all of the Headmaster portraits depict deceased individuals. As such, though it is never directly stated, it can be assumed that a Headmaster who leaves the position for other reasons will not have their portrait added until after their death.